$$(x^2 + x + 3$$), \; \text{domain: } (-\infty, \infty)$$

Question 1

Which of the following relations is a function?

Accepted Answer

$$\{(-4, 2), (-2, -1), (1, 2), (3, 4)\}$$

Question 2

Given the equation $$y^2 + 2x = 10$, is this a function? Why or why not?

Accepted Answer

No, because for some $$x$$ values there are two $$y$$ values.

Question 3

What is the domain of the function $$f(x) = \sqrt{x+4}$$? Express your answer in interval notation.

Accepted Answer

$$[-4, \infty)$$

Question 4

Which of the following equations represents a circle centered at $$(1, -2)$$ with radius $$1$$?

Accepted Answer

$$(x-1)^2$$ + $$(y+2)^2 = 1$

Question 5

If $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[8, \infty)$$

Question 6

Which transformation is represented by $$f(x) \rightarrow f(x-3) + 2$$?

Accepted Answer

Shift right 3 units, up 2 units

Question 7

Given $$f(x) = x^2$ + 1$$ and $$g(x) = x + 2$$, find $$(f+g)(x)$$ and its domain.

Accepted Answer

$$(x^2 + x + 3$$), \; 	ext{domain: } (-\infty, \infty)$$

Question 8

Which of the following is the correct function notation for $$y = 3x - 4$$?

Accepted Answer

$$f(x) = 3x - 4$$

Question 9

What is the result of reflecting the function $$f(x) = x + 2$$ over the x-axis?

Accepted Answer

$$h(x) = -f(x) = -x - 2$$

Question 10

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, \infty)$$

Question 11

Which of the following is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 9$

Question 12

If $$f(x) = \sqrt{x}$$ and $$g(x) = 3x - 6$$, what is the domain of $$f(g(x))$$?

Accepted Answer

$$[2, \infty)$$

Question 13

Which of the following describes a vertical stretch of $$f(x) by a $$factor of 2?

Accepted Answer

$$2f(x)$$

Question 14

Given $$h(x) = 2x^3$ - 4$$ and $$k(x) = x^2$ + 2$$, what is $$(h \cdot k)(x)$$?

Accepted Answer

$$2x^5$$ - $$4x^2$$ + $$2x^3 - 8$

Question 15

Which of the following is the correct standard form for a circle with center $$(0,1)$$ and radius $$3$$?

Accepted Answer

$$(x-0)^2$$ + $$(y-1)^2 = 9$

Question 16

If $$f(x) = x^2$ and g(x) = x-1$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$4$$

Question 17

Which of the following is the correct decomposition for $$h(x) = \sqrt{x-2}$$?

Accepted Answer

$$f(x) = \sqrt{x}, \; g(x) = x-2$$

Question 18

Given the general form $$x^2$$ + $$y^2 + 2x + 6y + 8 = 0$, what is the center and radius of the circle in standard form?

Accepted Answer

Center $$(-1, -3)$$, radius $$\sqrt{2}$$

Functions, Graphs, and Circles: Precalculus Study Notes

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